Rectangular Number in Java
In this section, we will learn what is a rectangular number and also create Java programs to check if the given number is a rectangular number or not. The rectangular number program is frequently asked in Java coding interviews and academics.
A rectangular number is a positive integer that can be arranged in rectangular forms. It is also called as pronic or oblong numbers.
In simple words, rectangular number is a special type of number that makes the shape of a rectangle using an array, where the elements are arranged based on rows and columns.
Rectangular Number Example
The number 2 is a rectangular number because it forms a rectangle of 1 row and 2 columns.
The number 6 is a rectangular number because it forms a rectangle of 2 row and 3 columns,
Similarly, the number 8 is a rectangular number because it forms a rectangle of 2 row and 4 columns.
Note: The number 4 is the only even number that is not a rectangular number, because it forms square with array of 2 rows and 2 columns.
Not only even, but some odd numbers can also form a rectangular shape. For example, the number 15 can form rectangle of 3 rows and 5 columns, as shown below.
Some other rectangular numbers are:
0, 2, 6, 12, 20, 30, 42, 56, 72, 90, 110, 132, 156, 182, 210, 240, 272, 306, 342, 380, 420 …
We observe that we can calculate nth rectangular number by using the following formula:
Rn = n(n + 1) or n2 + n
Let's find the 4th rectangular number.
Given number is 4.
Rn = n (n + 1)
Rn = n2 + n
R4 = (4)2 + 4
R4 = 20
Hence, the 4th rectangular number is 20.
Steps to Find Rectangular Number
Let's implement the above steps in a Java program.
Rectangular Number Java Program
Consider the following example to check whether given number is a rectangular number or not.
Find nth Rectangular Number
Consider following example where we print the nth rectangular number, the value of n is provided by the user.